Your customer - especially a first-time customer - will feel more comfortable if you let her/him know that you back up your work. You want to be sure that your customer doesn't think of you as just another of the many dirt-ball home services contractors out there, willing to say or do anything to separate customer from customer's money.
Particularly on tough wall2wall carpeting jobs, those where no matter what you do, the carpet is not going to look brand new when you're finished, I tell my customer that if she thinks that someone else might be able to clean it better, than she can - within a reasonable period of time - arrange to have this done. I further tell her that if she reports back to me that this other company did in fact get her better results, then I will refund to her what she paid me for the job, or the part of the job that was redone. But I tell her that if no real improvement is achieved, then I won't feel obligated to make the rebait. So we are now on kind of a double honor system. People like this offer you make, as it gives them more control than they normally have in dealing with contractors.
I make a similar offer with regard to area rugs. In this case I suggest that if results were somehow less than she had hoped, that she should feel free to send the rug out to an in-plant, deep immersion facility.
If, when the rug is returned to her, she agrees that the results are superior, than I would rebait to her what she had paid me for my work on that rug. Customers think twice about doing this, however, when you remind them that they will be charged in the vicinity of XXX dollars per sq. ft. by the in-plant rug cleaner, and that if there is no noticeable improvement, I will not be obliged to make a rebait, and she will have paid twice. In my area, XXX dollars is in the vicinity of $3 per sq. ft., sometimes more. To send out a 9 x 12 rug could end up costing my customer somewhere between $300 and $350. (I charge .90 - $1.00/sq. ft. for Orientals and other area rugs.)
Very few customers will actually put you to the test on this, but you will win their loyalty by being ready & willing to give them a fair deal.